VANENTER, ACD and FERNANDEZ, R and SOKAL, AD (1991) RENORMALIZATION TRANSFORMATIONS IN THE VICINITY OF 1ST-ORDER PHASE-TRANSITIONS - WHAT CAN AND CANNOT GO WRONG. PHYS REV LETT , 66 (25) 3253 - 3256.
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We reconsider the conceptual foundations of the renormalization-group (RG) formalism. We show that the RG map, defined on a suitable space of interactions, is always single valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the other hand, we prove in several cases that near a first-order phase transition the renormalized measure is not a Gibbs measure for any reasonable interaction. It follows that the conventional RG description of first-order transitions is not universally valid.
|Title:||RENORMALIZATION TRANSFORMATIONS IN THE VICINITY OF 1ST-ORDER PHASE-TRANSITIONS - WHAT CAN AND CANNOT GO WRONG|
|Keywords:||LATTICE SYSTEMS, MATHEMATICAL PROPERTIES, GAUGE-THEORY, PRESSURE, DIAGRAMS|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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